The Competitive Pickup and Delivery Orienteering Problem for Balancing Car-Sharing Systems

Layla Martin (), Stefan Minner, Diogo Poças () and Andreas S. Schulz ()
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Layla Martin: Operations, Planning, Accounting and Control, Eindhoven University of Technology, 5612 AZ Eindhoven, Netherlands
Diogo Poças: Operations Research, Technical University of Munich, 80333 Munich, Germany

Transportation Science, 2021, vol. 55, issue 6, 1232-1259

Abstract: Competition between one-way car-sharing operators is currently increasing. Fleet relocation as a means to compensate demand imbalances constitutes a major cost factor in a business with low profit margins. Existing decision support models have so far ignored the aspect of a competitor when the fleet is rebalanced for better availability. We present mixed-integer linear programming formulations for a pickup and delivery orienteering problem under different business models with multiple (competing) operators. Structural solution properties, including existence of equilibria and bounds on losses as a result of competition, of the competitive pickup and delivery problem under the restrictions of unit-demand stations, homogeneous payoffs, and indifferent customers based on results for congestion games are derived. Two algorithms to find a Nash equilibrium for real-life instances are proposed. One can find equilibria in the most general case; the other can only be applied if the game can be represented as a congestion game, that is, under the restrictions of homogeneous payoffs, unit-demand stations, and indifferent customers. In a numerical study, we compare different business models for car-sharing operations, including a merger between operators and outsourcing relocation operations to a common service provider (coopetition). Gross profit improvements achieved by explicitly incorporating competitor decisions are substantial, and the presence of competition decreases gross profits for all operators (compared with a merger). Using a Munich, Germany, case study, we quantify the gross profit gains resulting from considering competition as approximately 35% (over assuming absence of competition) and 12% (over assuming that the competitor is omnipresence) and the losses because of the presence of competition to be approximately 10%.

Keywords: car-sharing; competition; mixed-integer linear programming (search for similar items in EconPapers)
Date: 2021
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